Abstract: Suppose one is interested in estimating causal effects, in the presence of potentially unmeasured confounding using a valid instrumental variable. This study investigates the problem of making inferences about the average treatment effect when data are fused from two separate sources. Here, one data source contains information on the treatment and the other contains information on the outcome, while values for the instrument and a vector of baseline covariates are recorded in both. We provide a general set of sufficient conditions under which the average treatment effect is nonparametrically identified from the observed data law induced by data fusion, even when the data are from two heterogeneous populations, and derive the efficiency bound for estimating this causal parameter. For inference, we develop both parametric and semiparametric methods, including a multiply robust and locally efficient estimator that is consistent, even under partial misspecification of the observed data model. We illustrate the methods using simulations and an application on public housing projects.

Key words and phrases: Multiple robustness, two-sample inference, unmeasured confounding.